I would very much like to hear albaby’s take on this.

I haven't had a chance to read the opinion yet, so I've only been able to read some of the quick commentary about it. My impression is that the majority grounded its ruling on their conception of the scope of the Judicial power granted under the Constitution to the Court and the scope of the Judiciary Act of 1789 (which set up the lower courts).

Like the other three branches, the Court (ostensibly) only has the power that has been given it under the Constitution. Unlike the other two branches, the Constitution is very limited in describing what that power is. It's the "Judicial Power." But what is that power? Historically, the Court has understood the Judicial Power as the authority to resolve actual disputes between parties. That's why the Court has such weird (to lay people) requirements about standing - the Court has traditionally understood its role as not being a general interpreter of the law, but as an arbiter of actual cases between two parties that have a real dispute that the Court can actually decide and grant relief in.

So the majority in this decision chose to apply that to the injunction question by saying that the Constitutional power of the Court to order relief is limited to granting relief to the parties that are in front of it. To resolving the case. If the Court finds that Bob is causing damage to Alice by unlawfully doing X to her, the Court has the power to tell Bob to stop doing X to Alice. But even Bob is also doing X to Charlie, Charlie isn't before the Court (in this hypothetical). If getting Bob to stop doing X to Alice offers Alice complete and total resolution of her claim against Bob, then there's no basis for the Court to order Bob to do anything vis-a-vis Charlie. The Court's determination that X was unlawful might carry over to a future Bob-Charlie lawsuit - but the Court lacks power to order relief against Bob's future actions against Charlie in a lawsuit that only features Alice and Bob.

Congress has the power to give the judiciary broader powers than the bare minimum granted by the Constitution, and has done so in the Judiciary Act of 1789, but apparently the majority did not believe that they had granted the additional power necessary here.

I'm going to read the opinion over the weekend, but that's my initial take based on what I've read.